after shutdown iMac,later it will not start up anymore

you might be able to fix it yourself if it's just dusty. you will not be able to do a full job without opening it, which if it's still under warranty i do not recommend doing yourself. Using a can of compressed air, blow on the bottom of the iMac and the intake vent on the back of the imac (behind the foot). also blow some air into the exhaust, that's the long slit on hte back of the iMac. if you see lots of dust comming out you might want to get it opened and cleaned at an apple certified servicer.

Mayer is correct through in getting it checked at an Apple servicer, as if the dust is really bad, which at the point of overheating to shut down it most likely is, you might have some serious damage.